Modern semiconductor devices are often fabricated on an integrated-circuit (IC) chip. Generally, software tools may be implemented to design layouts of an IC chip at very small scales. Once a designed layout for an IC chip is finalized, the layout may be converted into a set of masks or reticles using an electron beam, ion beam or other suitable techniques. One or more semiconductor wafers may be patterned during one or more lithography processes using the set of masks so that the mask patterns are transferred to the wafers for fabricating semiconductor devices of the IC chip.
As more devices are incorporated on a single IC chip, the size of each device and the spacing between the devices (i.e., feature size) continues to decrease. For example, the feature size of an IC chip may be much smaller than the wavelength of light used for lithography (e.g., the resolution of the lithography). Multi-patterning lithography is often used to generate sub-resolution features on the IC chip. For example, a sequence of patterning processes, which may correspond to separate lithography exposures (e.g., with different masks) respectively, may be implemented to produce a sub-resolution pattern. Generally, an initial design layout is decomposed into multiple targets subject to certain design rules, and each target may correspond to a single mask. Such decomposition, or mask assignment, is called layout coloring, where different shapes in the initial layout are in different colors with the total number of available colors determined by the number of masks. For example, the initial layout includes shapes A and B and the distance between the shapes A and B is less than a predetermined limit. Accordingly, A and B have to be colored differently. That is, A and B have to be assigned to different masks.
However, a layout finalized based on certain design rules may not be reproduced on a semiconductor wafer for fabricating an IC chip. For example, light may diffuse to cause a sharp corner of a shape in the layout to appear round on the wafer. The shapes in the layout may be adjusted to correct for manufacturing idiosyncrasies and achieve better printability, which is often referred to as retargeting.